2T-POT Hawkes model for left- and right-tail conditional quantile forecasts of financial log-returns: out-of-sample comparison of conditional EVT models

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Conditional extreme value theory (EVT) methods promise enhanced forecasting of the extreme tail events that often dominate systemic risk. We present an improved two-tailed peaks-over-threshold (2T-POT) Hawkes model that is adapted for conditional quantile forecasting in both the left and right tails of a univariate time series. This is applied to the daily log-returns of six large cap indices. We also take the unique step of fitting the model at multiple exceedance thresholds (from the 1.25% to 25.00% mirrored quantiles). Quantitatively similar asymmetries in Hawkes parameters are found across all six indices, adding further empirical support to a temporal leverage effect in financial price time series in which the impact of losses is not only larger but also more immediate. Out-of-sample backtests find that our 2T-POT Hawkes model is more reliably accurate than the GARCH-EVT model when forecasting (mirrored) value-at-risk and expected shortfall at the 5% coverage level and below. This suggests that asymmetric Hawkes-type arrival dynamics are a better approximation of the true data generating process for extreme daily log-returns than GARCH-type conditional volatility; our 2T-POT Hawkes model therefore presents a better performing alternative for financial risk modelling.
Original languageEnglish
Pages (from-to)324-347
Number of pages24
JournalInternational Journal of Forecasting
Issue number1
Early online date28 Apr 2023
Publication statusPublished - 1 Jan 2024

Bibliographical note

Funding Information:
An earlier version of this paper was uploaded to the arXiv preprint server under the title ‘2T-POT Hawkes model for dynamic left- and right-tail quantile forecasts of financial returns: out-of-sample validation of self-exciting extremes versus conditional volatility’. We thank the Associate Editor of the International Journal of Forecasting and the two anonymous referees for their feedback on our original submission. Their comments greatly helped us improve the clarity of our arguments and the presentation of our results. M.F.T. acknowledges support from EPSRC (UK) Grant No. EP/R513155/1 and CheckRisk LLP.

Publisher Copyright:
© 2023 The Author(s)


  • Hawkes process
  • Conditional extreme value theory
  • Value at Risk
  • Expected Shortfall
  • Leverage effect
  • Value at risk
  • Expected shortfall
  • Hawkes processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Finance
  • Business and International Management


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